Question: Rewrite as a simplified fraction. ${2.7\overline{2} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 272.2222...\\ 10x &= 27.2222...\end{align*}}$ Subtracting the two equations, we have: ${90x = 245}$ ${x = \dfrac{245}{90}} $ ${x = \dfrac{49}{18}} \text{or} {2 \dfrac{13}{18}}$